Research on New Energy Power System Stability Situation Awareness Based on Index Screening and Dynamic Evaluation

Abstract

In order to integrate various operation information and accurately explore the operation situation of a power system, a dynamic comprehensive evaluation method considering index screening is proposed, and based on this, a situation awareness (SA) system based on the new energy power system is established. Firstly, aiming at the problem of information overlap among indicators, the existing indicator system of the new energy power system is quantitatively screened and reconstructed by the indicator screening method based on Measure of Sampling Adequacy (MSA) and Kaiser–Meyer–Olkin (KMO) test statistics. Afterwards, the dynamic evaluation method incorporating the subjective and objective is used to calculate the evaluation score and identify the stable operating state of the system. Finally, qualitative trend analysis and judgment are carried out on the evaluation scores, and the effect of power system situational awareness is verified by the improved IEEE 39 system. The results demonstrate that this method can be useful for improving the stability state sensing accuracy of a new energy power system.

1. Introduction

As an important carrier for the production, conversion, transmission, distribution, and use of electric energy, the stable operation of power systems containing new energy directly affects the quality and reliability of electric energy. Due to the expanding scale of new energy sources and an increasingly complex network structure, the uncertainty of grid operation status has been increasing [1], which has led to a number of large-scale power outages around the world, resulting in huge economic losses and adverse social impacts. Based on the above mentioned problems, the future change trend of the grid operation trajectory needs to be predicted to prevent major accidents and make the grid operation more efficient and safe, and scholars introduced the concept of situational awareness [2] to analyze the overall evolution trend of the system, using advanced technology to collect, process, and analyze the large-scale operation data of the power system containing new energy sources, to discover the operation condition of the grid in time, predict the development trend of the power grid operation condition, discover abnormal conditions and provide timely warnings, and assist decision makers in formulating control schemes to ensure stable system operation.

Situational awareness consists of three phases: information extraction, comprehension, and forecast [3]. The literature [4] introduces the main components and functional hierarchy of the grid situational awareness system and proposes a smart grid situational awareness model and conceptual design. The key parts of the grid stability operation situational awareness are situational understanding and situational prediction, which are manifested in the information acquisition stage to obtain system operation data in the grid database and in the understanding and prediction stage to construct a perfect index system and grid situational evaluation model through information integration and to summarize and predict the grid operation trajectory and development situation based on the evaluation results [5,6]. How to filter out effective features from the huge amount of data and to analyze and process them for the visualization and prediction of grid operation status is the main problem facing future research on grid stability operation situational awareness. The current research in the comprehension stage is used mainly to construct an evaluation index system that integrates various operation information and build a corresponding evaluation model to comprehensively evaluate each index of the grid operation status so as to identify the system operation status, diagnose the weakness of the grid, and grasp the direction of the grid status change. In terms of an evaluation index system, Sun et al. [7] established a flexibility index system with four indicators: attributes, constraints, loads, and structural flexibility. Porretta et al. [8] evaluated the adequacy and security of the high-capacity power system by considering generation and transmission faults, load changes, the economic dispatch of generation, security constraints, maintenance plans, and control actions implemented in emergency situations. Xia et al. [9] defined static voltage risk and transmission line overload risk indices to evaluate the fact that large-scale wind power integration into the grid brings serious uncertainties and operational risks to the safe operation of the power system. Zhou et al. [10] defined evaluation indexes for supply capacity reserve, supply capacity margin, and supply capacity balance and developed single-tier and inter-tier equipment evaluation models. The above study only analyzes a certain aspect of the grid and does not reflect the overall operation of the grid. Ge et al. [11] proposed a comprehensive evaluation framework and established an index system, including the equipment condition monitoring level, power quality monitoring level, grid reliability level, grid self-healing capability, grid renewable energy consumption level, etc. Maihemuti et al. [12] constructed a system of 28 operation indexes, including frequency stability, voltage stability, small signal stability, transient stability, etc., to make a comprehensive evaluation of the system’s operation condition and a comprehensive evaluation of the system’s operation status. In terms of comprehensive evaluation methods, Song et al. [13] made a comprehensive evaluation of the distribution network based on the cooperative game and trapezoidal cloud model. Zhang et al. [14] proposed the variable hesitation degree method to improve evaluation accuracy based on the intuitionistic fuzzy hierarchy analysis. In the work of Qian et al. [15], the energy analysis of a comprehensive energy system was carried out based on a combination of fuzzy hierarchical analysis and the inverse entropy weight method. Li et al. [16] proposed the G1–entropy weight method to determine the comprehensive weights and combined it with attribute identification theory to establish an evaluation model to evaluate the power quality. In addition, there are some common evaluation methods, such as the Analytic Hierarchy Process (AHP), the Preference Ranking Organization Method for Enrichment and Evaluations (PROMETHEE), the Elimination et Choix Traduisant la Realité (ELECTRE) [17], the Decision-Making Trial and Evaluation Laboratory (DEMATEL), the Analytic Network Process (ANP) [18,19], the Entropy Weight (EW) [20], the Simple Additive Weighting (SAW), the Grey Relational Analysis (GRA), the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the Multi-Objective Optimization on the Basis of Ratio Analysis (MOORA) [21]. By combining the subjective evaluation method and the objective evaluation method in the above methods, the combination weight is calculated. The combination of subjective and objective evaluation methods can attain a more reasonable judgment on the relative importance of the indicators by considering the interconnection between the indicators while paying attention to the discrete degree of the indicators. The above research has created remarkable achievements in the improvement of the evaluation index system and weight calculation method. Finally, in the prediction stage, most of the existing literature uses data prediction models to predict the comprehensive evaluation results [22,23] to realize the advance evaluation of the power system operation status so as to judge the development trend of the system’s stable operation status.

However, the structure of the power system is complex, and there are many indicators to represent various operating characteristics. The selection of indexes mostly relies on expert experience, and the correlation among indexes is not analyzed, resulting in an information overlap and errors in the evaluation results. At the same time, the power system is a dynamic system, and its operation data change constantly [24]. Although the evaluation method combining subjective and objective factors takes into account the expert’s experience and the situational information contained in the system operation data set, compared to the single subjective evaluation method, the accuracy of the evaluation is improved. However, the analysis of the static data set cannot meet the requirements of situational awareness.

The main contributions and outlines of this paper to improve on the above issues are shown below.

• Introducing qualitative trend analysis methods [25,26] into the situational awareness framework to visualize state change trends;
• In this paper, an index screening method based on Measure of Sampling Adequacy (MSA) and Kaiser–Meyer–Olkin (KMO) test statistics is proposed to screen the existing power system operation indexes and establish a stable operation situation awareness (SA) index system with low information overlap according to multiple operation criteria;
• The dynamic variable weight formula is proposed to dynamically change the weights according to the index values and to dynamically evaluate the operation status of the system by constructing a comprehensive evaluation method combining the intuitive fuzzy analysis hierarchy process and improved CRITIC;
• The effectiveness of the situational awareness framework in this paper is verified through simulation;
• This paper compares the state identification results of the comprehensive evaluation before and after the improvement of index screening and dynamic assignment, as well as the state identification results and sensitivity analysis results of the comprehensive evaluation methods proposed in the recent literature, and it verifies the superiority of the improved method proposed in this paper.

The rest of this article is organized as follows: Section 2 introduces the workflow of the situational awareness framework and the analysis method of qualitative trend analysis. Section 3 collects and introduces the common stable operation indicators and establishes the initial indicator set. The proposed indicator screening method is used to screen the indicators and construct the stable operation indicator system in this paper. Section 4 introduces the dynamic weighting evaluation model, combining improved CRITIC and an intuitive fuzzy analysis hierarchy process. Section 5 presents simulation results. Finally, Section 6 concludes this article.

2. Situational Awareness Framework for Power Systems

2.1. Theoretical Framework of Situational Awareness

The concept of situational awareness [27] first appeared in the space field, including two levels of situational awareness: understanding and prediction. After the introduction of the power system, it expanded to three aspects, including the information extraction of power grid data, an understanding of the system’s operational situation, and a prediction of future situations. The theoretical framework [28] is shown in Figure 1.

Situational awareness synthesizes system operation data, the environment, and other information on a certain timescale. It identifies the system’s operational state, analyzes the development trend of the operational state, and assists power workers in formulating control schemes and providing feedback to the system’s operation control. The key to situational awareness is making a scientific and accurate identification of the system’s situation, based on multi-source data.

2.2. Qualitative Trend Analysis

The identification of a power system situation can be defined as the determination of the system’s operating state and its state development trend. The index system is used to integrate information from many measurements taken during the power system’s running process, and the comprehensive evaluation method is used to calculate the evaluation score that represents the current running point of the system’s health level. The score is then compared to the score of an unstable state to judge the “good” and “bad” running states at that moment, and the situation level is divided according to the degree of instability. The change in trend of the evaluation score is identified by qualitative trend analysis, based on which the change in direction of the running state in a relatively short time is predicted. Qualitative trend analysis includes data interception and trend recognition.

2.2.1. Data Interception Based on Adaptive Sliding Time Window

The setting of the adaptive sliding time window [29] should consider the width of the window and the fitting threshold. The window width represents the amount of intercepted data, and the fitting threshold represents the threshold value at which the fitting function can be accepted. The initial width of the time window is set to $m$, and the fitting threshold is set to $R_N^2$. Further, $m$ system measurements are obtained in the same time interval, and the evaluation scores are calculated and imported into the window. The least squares method was used to linearly fit the scores in the window with the following fitting function:

$$\widehat{y}\left(t\right)=k\left(t-t_0\right)+{\widehat{y}}_0$$

(1)

where $t_0$ is the time window starting point; ${\widehat{y}}_0$ is the fitting value at time t; k is the slope; k > 0 p.u. indicates that the score has an upward trend in the period; k = 0 p.u. indicates that the score remains the same overall during the period; and k < 0 p.u. indicates that the score has a downward trend in the period.

The goodness of fit R² of the fitting function is calculated and compared with $R_N^2$. If the initial time window scores the fitting function R² > $R_N^2$, then continues to use this function to fit the score of the next moment, then the window width becomes $m+1$. Assuming that the corresponding fitting function features $t_{01}$, $y_{01}$, and k₁ have been calculated at time $t_1$, we can derive the following equation from Equation (1):

$$\widehat{y}\left(t_1+n\Delta t\right)=k_1\left(t_1+n\Delta t-t_{01}\right)+y_{01}$$

(2)

where $\Delta t$ is the sampling interval and $\left(n=1,2,3,\cdots \right)$ is the number of samples. The above equation represents the corresponding fitting function after continuing to fit n scores at time $t_1$. When R² ≤ $R_N^2$ stops, the data at the end of the time window at this moment are taken as the start data of the next time window, and the subsequent score fitting is entered.

If function R² ≤ $R_N^2$ is fitted in the initial time window, the window width is halved until R² > $R_N^2$ and the above data interception and fitting process is repeated.

2.2.2. Trend Identification

According to the slope of the fitting function of each section, the three basic trend primitives of rise, level, and fall [30] are matched to describe the changing trend of the stable operating state of the system.

2.3. The Main Symbols Used in This Paper

The main symbols that appear in the following text are shown in

Table 1. Stable situation indicator set.

Symbols	Meaning	Symbols	Meaning
KMO	Kaiser–Meyer–Olkin test statistics	$H_t$	renewable energy penetration
MSA	Measure of Sampling Adequacy	$Am$	active margin
SA	Situation Awareness	$Um$	static voltage stability margin
$d_i$	static safety distance	$C$	initial decision matrix
$L_C$	average transformer load ratio	$C^{\prime }$	standardized decision matrix
$L_a$	average branch load ratio	$D$	correlation coefficient matrix
$N_L$	$N-1$ branch ratio	$e_i$	conflict coefficient
$N_C$	$N-1$ transformer specific ratio	$w_i^{″}$	objective indicator weight
$SC$	short-circuit power flow over limit rate	$\mu (x)$	$x$ belongs to $A$ with affiliation
$p$	the partial correlation coefficient	$v(x)$	$x$ belongs to $A$ with non-affiliation
$THD$	total harmonic distortion rate	${\pi }_A\left(x\right)$	$x$ belongs to $A$ with hesitation degrees
$\Delta U$	node voltage offset	$B$	intuitionistic fuzzy judgment matrix
$\Delta F$	frequency offset	$\overline{B}$	product-type consistency judgment matrix
$Bo$	node voltage off-limit rate	$w_i^{\prime }$	subjective weights
$Fo$	the rate of power flow exceeding the limit	$W$	combined weight
$E_t$	the share of new energy generation	$W^{\prime }$	dynamic weighting
$Q_t$	new energy abandonment rate	$F$	comprehensive score
$I$	share of incoming active power from the external grid	$\underset{1\le i\le n}{\max }{L}_i$	maximum branch load rate

.

3. Establishment of Index System

The evaluation system is the basis for realizing a stable SA of the power system, and the construction of an efficient index system is the premise of comprehensive evaluation. In the information age, the dimensions of the power system dataset increase rapidly, and the indicators used to represent the operational characteristics also gradually increase. The information redundancy among indicators is serious; therefore, the scientific screening of indicators is key to research. The existing indicator system of the new energy power system is integrated, and the index set of the stability situation is preliminarily sorted out according to the different operating criteria and requirements of the system, as shown in

Table 2. Stable situation indicator set.

Order	Evaluation Indexes	Order	Evaluation Indexes
$A_1$	Steady-state security distance	$A_{11}$	Node voltage off-limit rate
$A_2$	Average transformer load ratio	$A_{12}$	Rate of power flow exceeding the limit
$A_3$	Maximum branch load rate	$A_{13}$	Carbon dioxide emission reduction
$A_4$	Average branch load ratio	$A_{14}$	Share of new energy generation
$A_5$	$N-1$ Branch ratio	$A_{15}$	New energy abandonment rate
$A_6$	$N-1$ Transformer-specific ratio	$A_{16}$	Renewable energy penetration
$A_7$	Short-circuit power flow over limit rate	$A_{17}$	Share of external grid incoming active power
$A_8$	Total harmonic distortion rate	$A_{18}$	Active power margin
$A_9$	Node voltage offset	$A_{19}$	Static voltage stability margin
$A_{10}$	Frequency offset

.

The security, reliability, and stability of the power system are inseparable. The stable operation of the system is the basis for ensuring the safety and reliability of the power supply, which is also the embodiment of the stable operation of the system. Therefore, the security and reliability indices are included in the stability situation index set of the system in this paper. According to the various requirements for the stable operation of the new energy power system, the physical significance and mathematical model of the indicators in Table 2 are divided into six categories for a corresponding introduction.

3.1. Index Definition

3.1.1. Steady-State Security Distance

The shortest distance from the operating point $P_{G0}\left(P_{G1}{}^0,P_{G2}{}^0,\cdot \cdot \cdot ,P_{Gn}{}^0\right)$ to the boundary of the static safety domain [31] of the branch $i$ reflects the ability of the branch to resist the volatility of the new energy output based on the balance of the branch load capacity and topological location. The formula is as follows:

$$\{\begin{array}{l}{d}_i=\min \Vert p_{\mathrm{g}}-P_{G0}\Vert \hfill \\ \mathrm{s}.\mathrm{t}. \{\begin{array}{l}{P}_{\mathrm{Gmin}}\le p_g\le P_{\mathrm{Gmax}}\hfill \\ -P_{\mathrm{L}\max }+G{P}_{\mathrm{D}}\le G_{\mathrm{g}}{p}_{\mathrm{g}}\le P_{\mathrm{L}\max }+G{P}_{\mathrm{D}}\hfill \\ 1^{\mathrm{T}}{p}_{\mathrm{g}}=1^{\mathrm{T}}{P}_{\mathrm{D}}\hfill \\ e_i^{\mathrm{T}}{G}_{\mathrm{g}}{p}_{\mathrm{g}}=P_{\mathrm{Lm},i}+e_i^{\mathrm{T}}G{P}_{\mathrm{D}}\hfill \end{array}\hfill \end{array}$$

(3)

where $P_{G0}$ is the current active power output vector of all generating units at a certain operating point; $p_{\mathrm{g}}$ is the extreme operating point to be obtained, located at the boundary of the static security domain; and $P_{\mathrm{Gmax}}$ and $P_{\mathrm{Gmin}}$ are the maximum and minimum active power output vectors of the generator, respectively. Further, $P_{\mathrm{Lmax}}$ is the limit transmission power vector of the branch; $G$ is the node branch transfer distribution factor matrix; $G_{\mathrm{g}}$ is the column corresponding to the generator node in $G$; $P_{\mathrm{D}}$ is the load node active vector; and $e_i$ is the unit vector ${\left[0,\dots ,0,1_{i\mathrm{th}},0,\dots ,0\right]}^T$. In this formula, the four constraint conditions respectively represent the active power output constraint, branch power flow constraint, and supply and demand balance constraint and ensure that the extreme operating point $p_{\mathrm{g}}$ makes the power flow of branch $i$ reach the operating limit. When no branch is overloaded, the branch of $d_i$ is the safety short board of the system.

3.1.2. Load Level

The average value of the ratio between the transformer’s output apparent power and its rated capacity within a certain period of time is called the average transformer load ratio. The formula is as follows:

$$L_C=\left({\displaystyle \sum _{j=1}^B{P}_j/S_j}\right)/B$$

(4)

where $P_j$ is the active power transmitted by transformer $j$; $S_j$ is the rated capacity of transformer $j$; and $B$ is the total number of transformers.

Maximum branch load rate:

$$\underset{1\le i\le n}{\max }{L}_i=P_i/P_{i\max }$$

(5)

where $P_i$ is the actual transmission power of branch $i$; $P_{i\max }$ is the limit transmission power of branch $i$; and $n$ is the total number of branches.

Average branch load ratio:

$$L_a=\frac{1}{n}{\displaystyle \sum _{i=1}^n\frac{P_i}{P_{i\max }}}$$

(6)

3.1.3. N − 1 Safety Criterion

In order to ensure that users obtain a continuous power supply in line with quality requirements, $N-1$ safety criterion is set up, and the $N-1$ branch ratio is defined as follows:

$$N_L=m_1/n$$

(7)

where $m_1$ is the number of branches that do not satisfy $N-1$ criterion.

The $N-1$ transformer specific ratio is also defined:

$$N_C=m_2/B$$

(8)

where $m_2$ is the number of transformers that do not satisfy the $N-1$ criterion.

3.1.4. Power Quality

The quality of power is directly related to the reliability, stability, and security of the power system, which is of great significance to the economic and social development of modern society.

Short-circuit power flow over limit rate is the proportion of branches whose power flow over-limit occurs when short-circuit fault occurs:

$$SC=m_3/n$$

(9)

where $m_3$ is the number of off-limit branches.

The total harmonic distortion rate is the harmonic content generated by the power electronic components or nonlinear loads after they are connected to the grid:

$$THD=\sqrt{{\displaystyle \sum _{z=2}^N{\left(\frac{G_z}{G_1}\right)}^2}}$$

(10)

where $G_z$ is the effective value of the $z$ harmonic component. Further, $I_z$ or $U_z$ are used to denote current or voltage, respectively. The total voltage distortion rate is studied in this paper.

The node voltage offset is the difference between the actual node voltage and the reference voltage, which indirectly reflects the system reactive reserve capacity:

$$\Delta U=u-u_0$$

(11)

where $u$ is the actual voltage and $u_0$ is the reference voltage.

The frequency offset is the difference between the actual generator frequency and the reference frequency after a fault, indirectly reflecting the active reserve capacity of the system:

$$\Delta F=f-f_0$$

(12)

where $f$ is the actual frequency and $f_0$ is the reference frequency.

The node voltage off-limit rate is the ratio of the number of node voltage overruns caused by scenery power fluctuations and load changes to the number of summary points:

$$Bo=m_4/e$$

(13)

where $m_4$ is the number of transgressing nodes and $e$ is the total number of nodes.

The rate of power flow exceeding the limit is the ratio of the number of tidal currents crossing the limit to the total number of branches caused by fluctuations in scenery output and load changes:

$$Fo=m_5/n$$

(14)

where $m_5$ is the number of crossing branches.

3.1.5. Cleanliness Requirements

The cleanliness index is a comprehensive indicator of environmental benefits and characterizes the sustainability of the power system. New energy generation gradually replaces traditional thermal power generation, resulting in less fossil fuel combustion and lower CO₂ emissions. In this paper, based on the conservation of carbon elements, it is introduced that for each unit of electricity generated by new energy units instead of thermal units, the power system generates a 0.997 kg reduction in carbon dioxide emissions at the power generation end.

It is assumed that in a regional new energy power system, the new energy units are wind power and photovoltaic generating units. The total installed capacity of the generating units is $P_{\mathrm{Z}}$, and the installed capacity of the wind power PV generating units are $P_{\mathrm{W}}$ and $P_{\mathrm{P}}$, respectively. At the moment $t$ the wind power PV generation is $P_{\mathrm{W}t}$ and $P_{\mathrm{P}t}$, respectively, and the total load is $L_{\mathrm{Z}t}$.

The share of new energy generation at that moment:

$$E_t=\left(P_{\mathrm{W}t}+P_{\mathrm{P}t}\right)/P_{\mathrm{Z}}$$

(15)

The new energy abandonment rate:

$$Q_t=\left(P_{\mathrm{W}}+P_{\mathrm{P}}-P_{\mathrm{W}t}-P_{\mathrm{P}t}\right)/\left(P_{\mathrm{W}}+P_{\mathrm{P}}\right)$$

(16)

Renewable energy penetration:

$$H_t=\left(P_{\mathrm{W}t}+P_{\mathrm{P}t}\right)/L_{\mathrm{Z}t}$$

(17)

The above indicators characterize the ability of a new energy power system in a region to utilize clean energy and visually reflect whether the system can meet the requirements of the times.

3.1.6. Safety Margin

The share of incoming active power from the external grid is the proportion of active power introduced to the external grid by a regional power system to maintain the balance of power supply and demand under the influence of wind power, PV output, and load volatility:

$$I=P_{in}/P_{\mathrm{Z}t}$$

(18)

where $P_{in}$ is the active power introduced at moment $t$.

The active margin is the safety margin of the active current of the system load node in the current state:

$$Am={\displaystyle \sum _{k=1}^K\left(\left|P_{k\max }-P_k\right|/P_k\right)}/K$$

(19)

where $P_{k\max }$ is the limit transmission capacity of the load node; $P_k$ is the active current of the load node; and $K$ is the total number of load nodes.

The static voltage stability margin is the margin of the system’s operating point from voltage instability, reflecting the reactive power reserve and the static voltage safety level of the system:

$$Um=\left(U_{k\max }-U_k\right)/U_{k\max }$$

(20)

where $U_{k\max }$ is the node limit voltage and $U_k$ is the actual node voltage.

3.2. Allowable Fluctuation Range of Indicators

According to the relevant provisions of international standards, the variation of some index data within a certain range is regarded as normal fluctuation and does not destroy the stable operating condition of the system. The indicators and allowable fluctuation ranges are shown in

Table 3. Allowable fluctuation range of indicators.

Evaluation Indexes	Order	Allowable Fluctuation Range	Reference Standards
Total Voltage Distortion Rate	$A_8$	0~8%	IEC 61000-2-2 [32]
Nodal Voltage Offset	$A_9$	±10%	EN 50160 [32]
Frequency Shift	$A_{10}$	±2%	IEC 61000-4-30 [33]

.

When processing the measurement data, only the part of the above three index values that exceeds the allowable range is calculated to reduce the influence of the masking phenomenon in the system stability analysis on the objectivity of the results.

The above indicators are listed according to national standards and the related literature. With the modernization of the power system and a high proportion of new energy and power electronic equipment, the indicators used to measure the operating characteristics of various aspects of the power system will gradually increase. Therefore, it is crucial to find a reasonable indicator screening method to perceive the operating status of the power system.

3.3. Evaluation Index Screening Based on MSA and KMO

The screening of indicators is carried out, firstly eliminating indicators of poor importance based on professional experience and then eliminating indicators with a high information overlap level. Since the indicators in this paper are selected in the evaluation system constructed by various experts and scholars, and their importance was generally high, the information overlap level of indicators is calculated directly. The MSA and KMO test statistics are used to analyze the indicator data set in the operation of the power system and eliminate the indicators with a high information overlap level. The statistic is the overall information overlap level of the indicator data set, and the specific screening steps are as follows:

Step 1: Calculate the KMO value of the indicator data set; the closer its value is to 1 p.u., the higher the information overlap of the indicator set. Allow there to be a total of n indicators in the data set and each indicator has m data. The formula is as follows:

$$KM{O}_n=\frac{{\displaystyle \sum _j^n{\displaystyle \sum _{i\ne j}^n{r}_{ij}{}^2}}}{{\displaystyle \sum _j^n{\displaystyle \sum _{i\ne j}^n{r}_{ij}{}^2}}+{\displaystyle \sum _j^n{\displaystyle \sum _{i\ne j}^n\frac{h_{ij}{}^2}{h_{ii}{h}_{jj}}}}}$$

(21)

where $r_{ij}$ is the Pearson correlation coefficient of indicator $i$ and indicator $j$ and $h_{ij}$ is the element in the inverse matrix $H={\left(h_{ij}\right)}_{n\times n}$ of the correlation coefficient matrix of the indicator set. When $KM{O}_n\ge 0.6$ p.u., the overlap of information for this set of indicators is too high, and it enters the screening process in Step 2 and vice versa in Step 3;

Step 2: The MSA value of each indicator is calculated, and the closer the value is to 1 p.u. the stronger the correlation between the indicator and the rest of the indicators, calculated with the following formula:

$$MS{A}_i=\frac{{\displaystyle \sum _{i\ne j}^n{r}_{ij}{}^2}}{{\displaystyle \sum _{i\ne j}^n{r}_{ij}{}^2}+{\displaystyle \sum _{i\ne j}^n\frac{h_{ij}{}^2}{h_{ii}{h}_{jj}}}}$$

(22)

Delete the $m$ data corresponding to the indicator with the largest MSA value in the data set, bring the remaining data set back to Step 1, and cycle the operation until the KMO value of the remaining indicator data set is less than 0.6 p.u., and then go to Step 3;

Step 3: Using partial correlation analysis to reduce the level of information overlap between indicators, if the partial correlation coefficient $p_{ij}$ meets $\left|p_{ij}\right|>r_0$, the indicator with the larger MSA between the two indicators is eliminated, where $p_{ij}=-h_{ij}/\sqrt{h_{ii}\times h_{jj}}$. The smaller the threshold $r_0$, the more indicators are eliminated and the lower the level of information overlap between indicators, and $r_0$ is set to 0.9 p.u. in this paper.

The indicators in Table 2 are screened according to the proposed MSA and KMO based indicator screening method, and the screening process is shown in

Table 4. Indicator screening process.

Number	$\mathit{K}\mathit{M}{\mathit{O}}_{\mathit{n}}$ Value	$\mathit{M}\mathit{S}{\mathit{A}}_{\mathit{i}}$ Maximum Indicator	$\mathit{M}\mathit{S}{\mathit{A}}_{\mathit{i}}$ Value	Results
19	0.736	$A_7$	0.867	Delete
18	0.689	$A_{13}$	0.829	Delete
17	0.629	$A_{15}$	0.759	Delete
16	0.359			Stop

and

Table 5. Absolute value of indicator bias correlation coefficient.

Indicators	${\mathit{A}}_1$	${\mathit{A}}_2$	${\mathit{A}}_3$	${\mathit{A}}_4$	…	${\mathit{A}}_{14}$	${\mathit{A}}_{16}$	${\mathit{A}}_{17}$	${\mathit{A}}_{18}$	${\mathit{A}}_{19}$
$A_1$	-	0.237	0.208	0.430	…	0.524	0.502	0.078	0.326	0.229
$A_2$	0.237	-	0.135	0.917 1	…	0.631	0.619	0.349	0.395	0.344
…	…	…	…	…	…	…	…	…	…	…
$A_{14}$	0.524	0.632	0.160	0.732	…	-	0.793	0.107	0.917 1	0.282
$A_{16}$	0.503	0.619	0.165	0.717	…	0.793	-	0.157	0.916 1	0.301
…	…	…	…	…	…	…	…	…	…	…
$A_{19}$	0.229	0.344	0.799	0.174	…	0.282	0.301	0.659	0.048	-

¹ Corresponding indicator does not meet the requirement of partial correlation coefficient.

. The indicator set data are the improved IEEE 39 system operation data, set under a typical day scenario in the arithmetic analysis.

The KMO value of the indicator data set are calculated, and since the initial KMO value is 0.736 p.u., which is greater than its set threshold, the indicators with larger MSA values are eliminated 1 by 1 until $KM{O}_n<0.6$ p.u. The calculation process is shown in Table 4; after the KMO value screening of the remaining 16 indicators in the indicator set, enter the indicators bias correlation analysis.

The results of the bias correlation analysis are shown in Table 5; we then deleted $A_4$, $A_{16}$, and $A_{18}$ according to Step 3. Calculate the partial correlation coefficient among the remaining indicators; the results are shown in

Table 6. Absolute value of partial correlation coefficient of residual index.

Indicators	${\mathit{A}}_1$	${\mathit{A}}_2$	${\mathit{A}}_3$	${\mathit{A}}_5$	${\mathit{A}}_6$	…	${\mathit{A}}_{12}$	${\mathit{A}}_{14}$	${\mathit{A}}_{17}$	${\mathit{A}}_{19}$
$A_1$	-	0.766	0.070	0.307	0.425	…	0.078	0.374	0.803	0.185
$A_2$	0.766	-	0.327	0.231	0.148	…	0.039	0.086	0.767	0.275
…	…	…	…	…		…	…	…	…	…
$A_{14}$	0.374	0.086	0.289	0.281	0.705	…	0.136	-	0.323	0.081
$A_{17}$	0.803	0.768	0.058	0.075	0.437	…	0.108	0.323	-	0.229
$A_{19}$	0.185	0.275	0.863	0.021	0.021	…	0.671	0.081	0.023	-

; and the remaining indicators meet $\left|p_{ij}\right|<0.9$ p.u.

From the screening results, it can be seen that the eliminated indicators are strongly correlated with the remaining indicators in a physical sense or mathematical model. The screened indicator set is classified according to different criteria to construct the operation status indicator system, as shown in

Table 7. Stability situation index system based on index screening.

Rule Layer		Index Layer	Index Attribute
Stability	$X_{11}$	Average transformer load ratio	Small-type
	$X_{12}$	Maximum branch load rate	Small-type
	$X_{13}$	Node voltage offset	Small-type
	$X_{14}$	Frequency offset	Small-type
Safety	$X_{21}$	Total voltage distortion rate	Small-type
	$X_{22}$	$N-1$ branch ratio	Small-type
	$X_{23}$	$N-1$ transformer ratio	Small-type
	$X_{24}$	Node voltage crossing rate	Small-type
	$X_{25}$	Rate of power flow exceeding the limit	Small-type
Adequacy	$X_{31}$	Share of external grid incoming active power	Small-type
	$X_{32}$	Share of new energy generation	Large-type
	$X_{33}$	Static voltage stability margin	Large-type
	$X_{34}$	Steady-state security distance	Large-type

.

4. Dynamic Integrated Evaluation Model

In order to synthesize the information contained in the expert experience and the actual measurement data of the indexes, the following is the dynamic evaluation of the index system using a comprehensive evaluation method combining subjective and objective.

4.1. Improvement of CRITIC Objective Empowerment Method

The CRITIC method [34] determines objective weights by calculating the comparison intensity and conflict degree of data among indicators comprehensively. In response to the problem that the traditional CRITIC objective evaluation method cannot account for the contrast intensity of indicators by standard deviation due to the different magnitudes and orders of data, the literature [35] introduces the Gini coefficient to measure the contrast intensity of indicators. To address the issue that the comparison intensity and conflicting multiplication widen the weight gap when synthesizing indicator information, this paper invokes the additive form [36] for indicator information synthesis. The calculation steps of the CRITIC method are as follows:

Step 1: Building a standardized decision matrix.

This is carried out by using the data collected by the measurement system to calculate the value of each indicator and construct the initial decision matrix $C={\left(c_{it}\right)}_{n\times m}$, where $c_{it}$ denotes the value of the $i$ indicator at moments $t$, $i\in [1,n]$, and $t\in [1,m]$. According to the following formula for the standardization of the deviation, the standardized decision matrix after the change is $C^{\prime }={\left(c_{it}^{\prime }\right)}_{n\times m}$.

If the indicator is large-type, the transformation is performed by Equation (23):

$$c_{it}^{\prime }=\frac{c_{it}-\min \left(c_i\right)}{\max (c_i)-\min (c_i)}$$

(23)

If the indicator is small-type, the transformation is performed by Equation (24):

$$c_{it}^{\prime }=\frac{\max \left(c_i\right)-c_{it}}{\max (c_i)-\min (c_i)}$$

(24)

where $\max \left(c_i\right)$ and $\min \left(c_i\right)$ denote the largest and smallest elements in row $i$ of the decision matrix $C$, respectively; $c_{it}^{\prime }$ is the value of indicator $i$ at moment $t$ after the normalization of the deviation;

Step 2: Calculation of the contrast strength factor.

The Gini coefficient of the indicator $\beta$ is calculated to characterize the intensity of the inter-indicator comparison:

$${\beta }_i=\frac{{\displaystyle \sum _{j=1}^n{\displaystyle \sum _{t=1}^m\left|c_{ij}^{\prime }-c_{it}^{\prime }\right|}}}{2n{\displaystyle \sum _{j=1}^n{c}_{ij}^{\prime }}}$$

(25)

The contrast intensity indicates the magnitude of the variability of the change in indicator $i$ over time, with respect to the variability of the rest of the indicators. The greater the variability, the more pronounced the change in the indicator and the larger the coefficient corresponding to the contrast intensity.

Step 3: Calculating the conflict degree factor.

The correlation coefficient matrix $D={\left(d_{\mathrm{ij}}\right)}_{n\times n}$ is calculated:

$$d_{ij}=\frac{{\displaystyle \sum _{k=1}^m\left(c_{ik}^{\prime }-{\overline{c}}_i^{\prime }\right)\left(c_{jk}^{\prime }-{\overline{c}}_j^{\prime }\right)}}{\sqrt{{\displaystyle \sum _{k=1}^m{\left(c_{ik}^{\prime }-{\overline{c}}_i^{\prime }\right)}^2}}\times \sqrt{{\displaystyle \sum _{k=1}^m{\left(c_{jk}^{\prime }-{\overline{c}}_j^{\prime }\right)}^2}}}$$

(26)

where ${\overline{c}}_i^{\prime }$ and ${\overline{c}}_j^{\prime }$ denote the mean values of indicator $i$ and indicator $j$ in $C^{\prime }$, respectively; $c_{ik}^{\prime }$ and $c_{jk}^{\prime }$ denote the deviation normalized values of indicator $i$ and indicator $j$ at moment $k$. Considering the existence of positive and negative correlations between indicators, the absolute value of the correlation coefficient is taken when quantifying the degree of the conflict coefficient, and the formula is as follows:

$$e_i=\frac{{\displaystyle \sum _j^n\left(1-\left|d_{ij}\right|\right)}}{{\displaystyle \sum _i^n{\displaystyle \sum _j^n\left(1-\left|d_{ij}\right|\right)}}}$$

(27)

The greater the conflict, the smaller the correlation coefficient between the indicators and the more representative the selected indicators are;

Step 4: Objective weighting determination.

To synthesize the indicator information, the pending coefficients are introduced to additively combine the intensity of comparison and the degree of conflict between indicators with the following formula:

$$\{\begin{array}{l}g=\frac{2}{n}{\displaystyle \sum _{i=1}^{n}i}{P}_i-\left(1+\frac{1}{n}\right)\\ \rho =\frac{n}{n-1}\times g\end{array}$$

(28)

The ordered vector $P$ is obtained by arranging the conflict vectors $e$ from the smallest to the largest, from which the discrepancy coefficient $g$ and the parameters to be determined $\rho$ are derived to obtain the combined information coefficient $q$:

$$q_i=\rho e_i+\left(1-\rho \right){\beta }_i$$

(29)

The following equation was used to determine the objective indicator weight:

$$w_i^{″}=q_i/{\displaystyle \sum _{i=1}^n{q}_i}$$

(30)

4.2. Intuitionistic Fuzzy Analytic Hierarchy Process

In order to portray the fuzzy nature of the objective world more delicately, the intuitionistic fuzzy analysis hierarchy process [13] considers three aspects of information, namely, affiliation, non-affiliation, and hesitation and is more flexible in dealing with fuzziness, uncertainty, etc. This method is used in this paper to assign subjective weights to indicators. The calculation steps are as follows:

Step 1: Constructing an intuitive fuzzy judgment matrix.

In the intuitionistic fuzzy set $A=\left\{(x,{\mu }_A(x),v_A(x))|x\in X)\right\}$, where $X$ is a non-empty set and $\mu (x)$ and $v(x)$ are the affiliation and non-affiliation degrees of $x$ belonging to $A$ in $X$, respectively, the following equation is satisfied:

$$\{\begin{array}{l}0\le \mu \left(x\right)+v\left(x\right)\le 1\\ 0\le \mu \left(x\right)\le 1\\ 0\le v\left(x\right)\le 1\end{array}$$

(31)

where $x$ belongs to $A$ with hesitation degrees ${\pi }_{\mathrm{A}}\left(x\right)$ and ${\pi }_{\mathrm{A}}\left(x\right)=1-{\mu }_{\mathrm{A}}(x)-v_{\mathrm{A}}(x)$. The hesitation degree can visualize the uncertainty of the expert when performing the evaluation of relative importance among indicators. When ${\pi }_{\mathrm{A}}\left(x\right)=0$, the intuitionistic fuzzy set degenerates into the traditional fuzzy set. In addition, $\left\{{\mu }_{\mathrm{a}},v_{\mathrm{a}},{\pi }_{\mathrm{a}}\right\}$ is a set of intuitionistic fuzzy numbers, for which a physical meaning is elaborated: when the fuzzy number is $\left\{0.6,0.1,0.3\right\}$, it can be considered that a total of 10 people vote for a decision, with 6 people supporting, 1 person opposing, and 3 people abstaining. The evaluation scale is constructed as shown in

Table 8. Definition of the scale of relative importance between indicators.

Qualitative Evaluation Language (Indicator $\mathit{i}$ Compared with Indicator $\mathit{j}$)	Intuitive Blurred Numbers
Quite important	(0.90, 0.10, 0.00)
Very important	(0.80, 0.15, 0.05)
Obviously important	(0.70, 0.20, 0.10)
Slightly important	(0.60, 0.25, 0.15)
Equally important	(0.50, 0.30, 0.20)
Slightly unimportant	(0.40, 0.45, 0.15)
Obviously unimportant	(0.30, 0.60, 0.10)
Very unimportant	(0.20, 0.75, 0.05)
Quite unimportant	(0.10, 0.90, 0.00)

, and experts are hired to make qualitative evaluations of the relative importance among the indicators of the same layer of the situational awareness system based on their experience, to construct an intuitionistic fuzzy judgment matrix B = (b_ij)_n×n;

Step 2: Consistency check.

This check is in order to test whether the constructed intuitionistic fuzzy judgment matrix is reasonable and whether the relative importance of each index is coordinated and compatible. The consistency test is now performed with the product-type consistency judgment matrix $\overline{B}={\left({\overline{b}}_{ij}\right)}_{n\times n}$. The specific method is as follows:

(1)

The intuitionistic fuzzy judgment matrix B = (b_ij)_n×n is used to construct the product-type consistency judgment matrix $\overline{B}={\left({\overline{b}}_{ij}\right)}_{n\times n}$.

When $j>i+1$, $\overline{B}={\left({\overline{\mu }}_{ij},\overline{v_{ij}}\right)}_{n\times n}$ is as follows:

$$\begin{array}{l}{\overline{\mu }}_{ij}=\frac{\sqrt{{\displaystyle \prod _{t=i+1}^{j-i-1}{\mu }_{it}}{\mu }_{tj}}}{\sqrt{{\displaystyle \prod _{t=i+1}^{j-1}{\mu }_{it}}{\mu }_{tj}}+\sqrt{{\displaystyle \prod _{t=i+1}^{j-1}\left(1-{\mu }_{it}\right)}\left(1-{\mu }_{tj}\right)}}\hfill \\ {\overline{\nu }}_{ij}=\frac{\sqrt{{\displaystyle \prod _{t-i-i}{v}_{it}}{v}_{tj}}}{\sqrt{{\displaystyle \prod _{t=i+1}^{j-1}{v}_{it}}{v}_{tj}}+\sqrt{{\displaystyle \prod _{t=i+1}^{j-1}\left(1-v_{it}\right)}\left(1-v_{tj}\right)}}\hfill \end{array}$$

(32)

When $j=i+1$ or $j=i$, ${\overline{b}}_{ij}=b_{ij}$, and when $j<i$, $\overline{B}={\left({\overline{v}}_{ji},\overline{{\mu }_{ji}}\right)}_{n\times n}$;

(2)

Set the threshold coefficient to $\tau$. Generally, $\tau$ is selected as 0.1 [37]. If $B$ and $\overline{B}$ satisfy $d\left(\overline{B},B\right)<\tau$, the intuitionistic fuzzy judgment matrix $B={\left(b_{ij}\right)}_{n\times n}$ is considered to meet the requirements. Further, $d$ is the distance-measure formula of $B$ and $\overline{B}$:

$$d\left(\overline{{\rm B}},B\right)=\frac{1}{2\left(n-1\right)\left(n-2\right)}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\left(|{\overline{\mu }}_{ij}-{\mu }_{ij}|+|{\overline{v}}_{ij}-v_{ij}|+|{\overline{\pi }}_{ij}-{\pi }_{ij}|\right)}}$$

(33)

If $d\left(\overline{B},B\right)\ge \tau$, the judgment matrix does not pass the test; introduce the correction factor $\delta \in [0,1]$ to make the corresponding adjustment to the judgment matrix through Equation (34). The actual size of $\delta$ can be selected by a human according to the actual situation, so that the corrected judgment matrix $B^{\prime }={\left(b_{ij}^{\prime }\right)}_{n\times n}$, $b_{ij}^{\prime }=\left({\mu }_{ij}^{\prime },v_{ij}^{\prime }\right)$ meets the consistency test requirements.

$${\omega }_i=\left(\frac{{\displaystyle \sum _{j=1}^n{\mu }_{ij}}}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\left(1-v_{ij}\right)}}},1-\frac{{\displaystyle \sum _{j=1}^n\left(1-{\mu }_{ij}\right)}}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{v}_{ij}}}}\right)$$

(34)

Step 3: Subjective weighting determination.

For the matrix $B$ or $B^{\prime }$ satisfying the consistency judgment, the weight vector $\omega ={\left[{\omega }_1,{\omega }_2,{\omega }_3,\cdot \cdot \cdot ,{\omega }_n\right]}^T$ between indicators of the same layer is obtained from Equation (35).

$${\omega }_i=\left(\frac{{\displaystyle \sum _{j=1}^n{\mu }_{ij}}}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\left(1-v_{ij}\right)}}},1-\frac{{\displaystyle \sum _{j=1}^n\left(1-{\mu }_{ij}\right)}}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{v}_{ij}}}}\right)$$

(35)

The absolute weight of any second-level indicator $t$ is obtained by applying the multiplication algorithm of the intuitionistic fuzzy set in Equation (36) after the first and second-level indicators are assigned with the weights of Equation (35) at the same time.

$${\omega }_k\otimes {\omega }_t=\left({\mu }_k\times {\mu }_t,v_k+v_t-v_k\times v_t\right)$$

(36)

where ${\omega }_t$ indicates the weight of secondary indicator $t$ and ${\omega }_k$ indicates the weight of primary indicator $k$ to which secondary indicator $t$ belongs.

At this point, the weights are still in the form of intuitionistic fuzzy numbers, denoted as ${\omega }_i=\left({\stackrel{⌢}{\mu }}_i,{\stackrel{⌢}{v}}_i\right)$. The weights are converted into single-valued form by introducing the scoring function H (${\omega }_i$), as shown in Equation (37).

$$w_i^{\prime }=\frac{H\left({\omega }_i\right)}{{\displaystyle \sum _{j=1}^{n}H\left({\omega }_i\right)}}=\frac{\frac{\stackrel{⌢}{\mu }}{2-{\stackrel{⌢}{\mu }}_i-{\stackrel{⌢}{v}}_i}}{{\displaystyle \sum _{i=1}^n\frac{\stackrel{⌢}{\mu }}{2-{\stackrel{⌢}{\mu }}_i-{\stackrel{⌢}{v}}_i}}}$$

(37)

The subjective weights of each indicator are obtained from the above equation. Combine the characteristics of subjective and objective weight assignments to calculate the portfolio weights.

4.3. Subjective and Objective Dynamic Integrated Empowerment

The relative entropy concept is applied to measure the difference between the weights obtained by the subjective and objective assignment methods and the combined weights. This is done so that the sum of the relative entropy of the combined weights and the weights of the two assignment methods is minimized, thereby preserving the distribution characteristics of the index weights obtained by different assignment methods.

The mathematical model of the combined weights is established as follows:

$$\{\begin{array}{l}\min S(a,b)={\displaystyle \sum _{i=1}^n{W}_i}\ln \left(\frac{W_i}{w_i^{\prime }}\right)+{\displaystyle \sum _{i=1}^n{W}_i}\ln \left(\frac{W_i}{w_i^{″}}\right)\\ s.t.\hspace{1em}\hspace{1em}a+b=1\hspace{1em}\hspace{1em}{W}_i=a{w}_i^{\prime }+b{w}_i^{″}\end{array}$$

(38)

where $W_i$ is the combined weight of indicator $i$; $S(a,b)$ is the relative entropy; $w_i^{\prime }$ and $w_i^{″}$ are the subjective and objective weights, respectively.

The improved CRITIC method determines the static weights of indicators by analyzing the static dataset of indicators. However, as time passes, the measurement information of the power system is constantly updated. If the value of an indicator changes drastically under the static weight, and the corresponding weight of the indicator is small, the evaluation results may not respond obviously to this distortion phenomenon, and the accuracy of situational awareness cannot be guaranteed. To address this issue, a variable weighting method is introduced to change the indicator weights using the measurement data. The dynamic weighting formula for each indicator is as follows:

$$W_i^{\prime }=\frac{W_i\times S_i}{{\displaystyle \sum _{i=1}^n{W}_i\times S_i}}$$

(39)

where $W_i$ is the index weight calculated by the combination assignment method; $S_i$ is the variable weight equilibrium function.

The exponential type state variable weight vector is widely used for its advantages such as strong fitting and flexible setting, and the variable weight equilibrium function is set in the paper as follows:

$$S_i=\exp \alpha \left|\frac{c_{ik}-{\overline{c}}_i}{{\overline{c}}_i}\right|$$

(40)

where ${\overline{c}}_i$ is the average value of the indicator data, and ${\overline{c}}_i$ changes after each update of the indicator data; $\alpha$ is a given constant coefficient whose value determines the weight differentiation after variable weighting, and $\alpha =0.5$ p.u. is taken in the text.

4.4. Evaluation Score

At a certain moment, the system index data are normalized to obtain vector $Z={\left[z_1,z_2,\cdot \cdot \cdot ,z_n\right]}^T$ with weight $W^{\prime }={\left[W_1^{\prime },W_2^{\prime },\cdot \cdot \cdot ,W_n^{\prime }\right]}^T$. The comprehensive score at the current moment is $F=Z^T\times W^{\prime }$ and $F\in \left[0,1\right]$. The closer $F$ is to 1, the better the system operation status is.

According to the above steps, the dynamic evaluation process is shown in Figure 2.

The evaluation model in this paper takes into account expert experience and the information contained in the system operation data. It considers the dynamic changes in the dynamic system operation status and improves the traditional static evaluation model to meet the dynamic and accurate requirements of power system situational awareness.

4.5. The Flow of the Situational Awareness

Step 1: Collect common stability operation indicators to establish initial indicator sets and calculate indicator values using relevant data from the power system;

Step 2: Standardize the indicator values, enter the indicator selection process, and use the remaining indicators to create a system of indicators;

Step 3: Using the comprehensive evaluation method in the text to calculate the weight of the combination of indicators, the dynamic weight at each moment is obtained through the dynamic variable weight formula;

Step 4: Using the dynamic weights and the standardized values of the indicators at each moment, the dynamic score is calculated. This is achieved by introducing qualitative trend analysis to extract trends in fractions to determine trends in the steady-state operation of the system.

The flow of the situational awareness process in this paper is shown in Figure 3.

4.6. Data Acquisition Intervals for Situational Awareness

This paper investigates the impact of “source-load” volatility on the steady state of operation, focusing on indicators that are strongly influenced by wind power, photovoltaic, and load changes, such as voltage stability margins and static safety distance. Because the “source load” fluctuation curve has a clear trend, and the indicator values are strongly correlated with the “source load” fluctuation, the time interval set for obtaining the indicator data is relatively large. When studying the impact of the operation of a high percentage of the system’s power electronics or the cutting of a large capacity unit on the stable operating state of the power system, the focus is on indicators with a high frequency of data fluctuations, such as distortion rates or frequency shifts, and sampling times need to be synchronized with measurement devices such as PMUs.

5. Example Analysis

In this section, we employ the modified IEEE 39 node system to conduct simulation analysis. Specifically, we substitute the conventional thermal power units located at nodes 35, 36, and 37 of the original system with a 650 MW photovoltaic plant, a 560 MW wind plant, and a 540 MW wind plant, respectively. By varying the output of the power sources and the load level, we investigate the impact of “source-load” uncertainty on the stable operation of the new energy power system. To this end, we normalize the typical daily load and active output data [38] using the maximum load level and the respective installed capacity of the generating units as base values and obtain the fluctuation curves depicted in Figure 4, which we consider the “source load” fluctuation curve from previous predictions. Based on these curves, we calculate various operating parameters under the fluctuation of the “source load” of the improved IEEE 39 system using Powerworld software.

5.1. Stable Operational SA under the “Source Load” Fluctuation

The sampling interval is set at 15 min intervals, and the “source load” data is transmitted to Powerworld for tidal current calculation and static safety analysis. This process results in the acquisition of operational data for each index. The dynamic comprehensive evaluation method is employed to compute the initial and dynamic weights for each indicator, as depicted in Figure 5 and Figure 6, respectively. Additionally, Figure 7 displays the rate of change for each indicator’s data.

The rate of change of data in Figure 6 is computed using equation $\left|(c_{ik}-{\overline{c}}_i)/\overline{c}\right|$. Indicators $X_{13}$, $X_{14}$, $X_{21}$, and $X_{24}$ have 0 values during the simulation; thus, no dynamic change of weight is applied to them. From Figure 6 and Figure 7, it is clear that the dynamic weight change of a particular indicator is influenced by both its own rate of change and its relative rate of change with respect to the remaining indicators. If an indicator with a small initial weight experiences a significant change in data at a certain point, its weight will increase significantly, thereby improving the perceived accuracy of this destabilizing factor. During a given period, multiple factors may cause the system to operate in an unstable state simultaneously. The more significant the change in the index data related to these factors, the higher the weight’s value after the weight change and the greater the impact on the state score. Therefore, insignificant changes in the value can be overlooked when analyzing the unstable state during a certain period of time.

In the simulation, there are 10 periods when the branch tide exceeds the limit, the power supply and demand are unbalanced, or the safety criterion is met at a low rate, which destabilizes the system’s operation. The instability periods and the main instability factors are shown in

Table 9. Set of unstable states.

Time Period	Major Destabilizing Factors	Maximum Rate of Change (%)
2:15~2:45	Increases in external grid incoming active power	4.71
6:00~6:30	$N-1$ branch increase	50
8:00~8:45	$N-1$ branch circuit increase	56.5
11:00~12:00	Branch tide crosses the line	100
12:45~13:15	Static safety distance decreases	29.3
13:15~13:30	Static safety distance decreases	3.4
16:45~17:15	$N-1$ transformer increase	75
19:00~20:00	Branch tide crosses the line	100
20:45~21:15	Static safety distance decreases	18.8
22:45~23:30	$N-1$ transformer increase	33.3

.

This is followed by applying the situational awareness method in the text to calculate the stability state score under a typical daily scenario and performing a qualitative trend analysis of the score; the results are shown in Figure 8; set $R_N^2=0.85$ p.u.

The slope $S$ of each fitting function is matched with 3 basic trend primitives: set $\left|S\right|\le 0.01$ p.u. corresponding to the horizontal primitive A, $S>0.01$ p.u. corresponding to the rising primitive B, and $S<-0.01$ p.u. corresponding to the falling primitive C. The trend primitive sequence in Figure 5 is ACACAABCBCBCBCBCBCBCBCCBAA. The destabilization periods and the corresponding trend primitives are shown in

Table 10. Instability period and trend primitive comparison table.

Time Period	Trending Primitives	Time Period	Trending Primitives
2:15~2:45	C	13:15~13:30	C
6:00~6:30	C	16:45~17:15	C
8:00~8:45	C	19:00~20:00	C
11:00~12:00	C	20:45~21:15	C
12:45~13:15	C	22:45~23:30	C

.

As seen in Table 10, there is a decreasing primitive C in the trend of the score change in all 10 time periods when the system is in an unstable state, characterizing the system’s operating point toward the unstable state operation. Combining the trend identification results with Figure 4, the analysis shows that during the time period from 2:15 to 2:45, the load level rises, and the wind power output decreases, leading to an increase in the incoming power from the external grid and a decrease in the state score. Between 6:00 and 9:00, the system active power in the region is insufficient, the number of branches that do not satisfy the $N-1$ criterion increases, and the system state has a clear trend to become worse. As the load level continues to rise, the tidal current crosses the limit at node 6–31 at 11:00, and the stable operation of the system is destroyed; after 12:00, the cross-limit branch returns to normal and the state score increases. The trend of the score is fluctuating. At 16:45~17:15, the “Source load” fluctuates sharply, and the number of $N-1$ transformers increase. Further, 19:00 is the evening peak of electricity consumption; the system has branch tide over the limit, the static safety distance decreases, and the number of $N-1$ transformers increases. The stable operation state is destroyed again. Under the situational awareness model in this paper, 10 operating state variation trends are accurately extracted, and the dispatcher can make corresponding control decisions with this trend information.

It can be seen that the method in this paper can effectively identify the trend of the stable operation state of the grid. When the active power output of renewable energy generation is low, the fluctuations of wind power, photovoltaic, and load will affect the active power margin, load share, and static safety distance of the system; however, the system can still maintain a relatively stable operation state. However, when the active power output of renewable energy generation is high, the fluctuation of wind power, photovoltaic, and load will cause tidal overrun faults, which will lead to equipment damage, power outages, and other power accidents. Dispatchers can forecast the index data and apply the text situational awareness method to identify the system’s stable operation status and change trend, and they can adjust the planned output of renewable energy units and the rotating reserve capacity of thermal power units in advance, so as to ensure the stable operation of the power system.

5.2. Comparison of Situational Awareness Results under Different Evaluation Methods

To verify the perception accuracy of the situational awareness model in this paper, the dynamic and static evaluation methods before and after index screening are compared, and the results are shown in Figure 9.

In Figure 9, the number represents the count of extracted unstable states. Only the dynamic evaluation method filtered by indicators can extract the decreasing primitive C in each unstable operation state, whereas other methods have insufficient perceptual accuracy due to data redundancy among indicators or static evaluation not adapted to the dynamic system. The order of the perceived accuracy of the unstable operation state is higher for the evaluation method with filtered indicators than for the evaluation method without filtered indicators, and the dynamic assignment is higher than the static assignment. In summary, it can be proven that the stability perception model based on index screening and dynamic evaluation can effectively extract the change trend of the system operation point to the instability state, and the perception effect is good.

To further validate the effectiveness and perceptual accuracy of the methods in this paper, the comprehensive evaluation methods in the comprehension phase of the situational awareness framework are replaced with the EW–TOPSIS method [39], EW–AHP method [40], AHP–TOPSIS method [41], and ICRITIC–EW combined with GRA–TOPSIS method [42], which have recently appeared in the literature and the perceptual accuracy is analyzed. The results are displayed in Figure 10.

A comparative analysis of the four evaluation results in the above figure with the evaluation results of the comprehensive evaluation method proposed in this paper in Figure 9 shows that the evaluation scores of the different methods showed approximately the same trend; however, the number of identified instability intervals differed. ICRITIC–EW combines the GRA–TOPSIS and EW–TOPSIS methods, combining the characteristics of multiple objective evaluation methods to assign weights, identifying relatively unstable states, however ignoring expert experience, resulting in relatively important indicators being assigned lower weight values, making the composite score less sensitive to changes in their values. The EW–AHP method and the AHP–TOPSIS method both combine the advantages of subjective and objective weighting methods and can effectively reflect the numerical changes of important indicators; however, it does not consider the continuity of state changes, and the trend of the identified state changes is not obvious. The comprehensive evaluation method proposed in this paper combines the advantages of subjective and objective evaluation with indicator screening and a dynamic assignment of weights to reduce data redundancy while enabling the weights of each indicator to be dynamically adjusted according to the rate of change of values, making the evaluation results more sensitive to numerical fluctuations of indicators with smaller weights with obvious trends of state changes and a relatively high resolution.

5.3. Sensitivity Analysis of Comprehensive Evaluation Methods in Texts

Sensitivity analysis refers to observing changes in the composite evaluation score by adjusting the values of the indicators. The objective of the model improvement in this paper is to enable the evaluation scores to reflect the dramatic changes in the data for the less weighted indicators. From the 13 secondary indicators, 3 indicators with small initial weights were selected for sensitivity analysis, so that the index value changed between $\pm 50\%$. The sensitivity analysis curve is calculated, as shown in Figure 11.

Analysis of Figure 11 shows that the proposed method in this paper can effectively identify the changes in rising or falling values of individual indicators, and its sensitivity is the highest among the five evaluation methods. It can be seen that the situational awareness model proposed in this paper can effectively identify the abnormal fluctuation of a certain index and enhance the identification of the unstable operation status of the system.

6. Conclusions

In this research work, the main contribution of this paper is to propose a comprehensive evaluation method that takes subjective and objective factors into account, based on the screening and dynamic weighting of indicators to improve the accuracy of the understanding of the stability of power system operation.

(1)

Starting from a situational awareness framework, we describe the process of applying situational awareness theory to the identification of the operational state of a power system;

(2)

A comprehensive evaluation method is used to identify the stable operating state of the system, and an indicator screening method combining KMO and MSA is proposed to screen current indicators. Additionally, a comprehensive evaluation method is proposed to adjust indicator weights according to the rate of change of indicator data, and a qualitative trend analysis method is introduced to improve visualization;

(3)

The effectiveness of the situational awareness method in this paper is verified through simulation analysis. A comparison with the operational status identification results of the pre-improvement method and the different evaluation methods recently proposed verifies the high sensing accuracy of the comprehensive evaluation method in this paper. A sensitivity analysis of the comprehensive evaluation model in this paper verifies that the evaluation scores of the model are also sensitive to indicators with small initial weights.

The aim of this paper is to provide a supportive decision-making tool for power system decision-makers. The originality of this paper lies in its proposal of a quantitative screening method for indicators and a dynamic empowerment improvement of the static evaluation model to make it applicable to the situational awareness framework. Future work should focus on the development of high-accuracy situational prediction methods and further improvements to the proposed situational understanding model.